# Properties

 Label 855.2.k.j.676.2 Level $855$ Weight $2$ Character 855.676 Analytic conductor $6.827$ Analytic rank $0$ Dimension $12$ CM no Inner twists $2$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [855,2,Mod(406,855)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(855, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("855.406");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$855 = 3^{2} \cdot 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 855.k (of order $$3$$, degree $$2$$, minimal)

## Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

 Self dual: no Analytic conductor: $$6.82720937282$$ Analytic rank: $$0$$ Dimension: $$12$$ Relative dimension: $$6$$ over $$\Q(\zeta_{3})$$ Coefficient field: $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{12} - 3 x^{11} + 13 x^{10} - 10 x^{9} + 44 x^{8} - 20 x^{7} + 119 x^{6} + 13 x^{5} + 83 x^{4} + 14 x^{3} + 46 x^{2} + 12 x + 4$$ x^12 - 3*x^11 + 13*x^10 - 10*x^9 + 44*x^8 - 20*x^7 + 119*x^6 + 13*x^5 + 83*x^4 + 14*x^3 + 46*x^2 + 12*x + 4 Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 676.2 Root $$-0.398236 + 0.689765i$$ of defining polynomial Character $$\chi$$ $$=$$ 855.676 Dual form 855.2.k.j.406.2

## $q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(-0.898236 + 1.55579i) q^{2} +(-0.613656 - 1.06288i) q^{4} +(-0.500000 + 0.866025i) q^{5} -3.41478 q^{7} -1.38811 q^{8} +O(q^{10})$$ $$q+(-0.898236 + 1.55579i) q^{2} +(-0.613656 - 1.06288i) q^{4} +(-0.500000 + 0.866025i) q^{5} -3.41478 q^{7} -1.38811 q^{8} +(-0.898236 - 1.55579i) q^{10} +4.35669 q^{11} +(-2.49135 - 4.31514i) q^{13} +(3.06728 - 5.31268i) q^{14} +(2.47416 - 4.28538i) q^{16} +(-0.0290433 + 0.0503046i) q^{17} +(-1.10304 - 4.21703i) q^{19} +1.22731 q^{20} +(-3.91334 + 6.77810i) q^{22} +(0.216041 + 0.374194i) q^{23} +(-0.500000 - 0.866025i) q^{25} +8.95127 q^{26} +(2.09550 + 3.62951i) q^{28} +(2.74750 + 4.75882i) q^{29} -0.592945 q^{31} +(3.05666 + 5.29428i) q^{32} +(-0.0521756 - 0.0903707i) q^{34} +(1.70739 - 2.95728i) q^{35} +6.62060 q^{37} +(7.55160 + 2.07179i) q^{38} +(0.694056 - 1.20214i) q^{40} +(0.0818718 - 0.141806i) q^{41} +(3.00242 - 5.20034i) q^{43} +(-2.67351 - 4.63066i) q^{44} -0.776222 q^{46} +(-5.54529 - 9.60473i) q^{47} +4.66070 q^{49} +1.79647 q^{50} +(-3.05766 + 5.29603i) q^{52} +(-2.69971 - 4.67603i) q^{53} +(-2.17835 + 3.77300i) q^{55} +4.74009 q^{56} -9.87163 q^{58} +(-1.72248 + 2.98342i) q^{59} +(-2.15698 - 3.73600i) q^{61} +(0.532604 - 0.922498i) q^{62} -1.08574 q^{64} +4.98270 q^{65} +(3.39217 + 5.87541i) q^{67} +0.0712905 q^{68} +(3.06728 + 5.31268i) q^{70} +(4.20501 - 7.28329i) q^{71} +(5.84804 - 10.1291i) q^{73} +(-5.94686 + 10.3003i) q^{74} +(-3.80532 + 3.76021i) q^{76} -14.8771 q^{77} +(-3.64303 + 6.30991i) q^{79} +(2.47416 + 4.28538i) q^{80} +(0.147080 + 0.254751i) q^{82} +16.1185 q^{83} +(-0.0290433 - 0.0503046i) q^{85} +(5.39377 + 9.34228i) q^{86} -6.04757 q^{88} +(-5.59024 - 9.68258i) q^{89} +(8.50740 + 14.7352i) q^{91} +(0.265150 - 0.459252i) q^{92} +19.9239 q^{94} +(4.20357 + 1.15325i) q^{95} +(-4.47355 + 7.74842i) q^{97} +(-4.18641 + 7.25107i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$12 q - 3 q^{2} - 5 q^{4} - 6 q^{5} + 4 q^{7} + 12 q^{8}+O(q^{10})$$ 12 * q - 3 * q^2 - 5 * q^4 - 6 * q^5 + 4 * q^7 + 12 * q^8 $$12 q - 3 q^{2} - 5 q^{4} - 6 q^{5} + 4 q^{7} + 12 q^{8} - 3 q^{10} - 8 q^{13} - 10 q^{14} - 3 q^{16} - 4 q^{17} - 6 q^{19} + 10 q^{20} + 2 q^{23} - 6 q^{25} + 40 q^{26} - 26 q^{28} - 4 q^{29} + 24 q^{31} - 15 q^{32} + 7 q^{34} - 2 q^{35} + 29 q^{38} - 6 q^{40} - 12 q^{41} - 4 q^{43} - 6 q^{44} + 48 q^{46} - 6 q^{47} + 32 q^{49} + 6 q^{50} - 20 q^{52} - 26 q^{53} + 44 q^{56} - 20 q^{58} - 16 q^{59} + 20 q^{61} + 25 q^{62} + 28 q^{64} + 16 q^{65} - 12 q^{67} - 54 q^{68} - 10 q^{70} + 8 q^{71} - 4 q^{73} + 16 q^{74} - 66 q^{76} - 48 q^{77} - 12 q^{79} - 3 q^{80} + 26 q^{82} + 44 q^{83} - 4 q^{85} + 44 q^{86} - 32 q^{88} + 8 q^{89} + 2 q^{91} - 36 q^{92} - 14 q^{94} + 6 q^{95} + 30 q^{97} - 49 q^{98}+O(q^{100})$$ 12 * q - 3 * q^2 - 5 * q^4 - 6 * q^5 + 4 * q^7 + 12 * q^8 - 3 * q^10 - 8 * q^13 - 10 * q^14 - 3 * q^16 - 4 * q^17 - 6 * q^19 + 10 * q^20 + 2 * q^23 - 6 * q^25 + 40 * q^26 - 26 * q^28 - 4 * q^29 + 24 * q^31 - 15 * q^32 + 7 * q^34 - 2 * q^35 + 29 * q^38 - 6 * q^40 - 12 * q^41 - 4 * q^43 - 6 * q^44 + 48 * q^46 - 6 * q^47 + 32 * q^49 + 6 * q^50 - 20 * q^52 - 26 * q^53 + 44 * q^56 - 20 * q^58 - 16 * q^59 + 20 * q^61 + 25 * q^62 + 28 * q^64 + 16 * q^65 - 12 * q^67 - 54 * q^68 - 10 * q^70 + 8 * q^71 - 4 * q^73 + 16 * q^74 - 66 * q^76 - 48 * q^77 - 12 * q^79 - 3 * q^80 + 26 * q^82 + 44 * q^83 - 4 * q^85 + 44 * q^86 - 32 * q^88 + 8 * q^89 + 2 * q^91 - 36 * q^92 - 14 * q^94 + 6 * q^95 + 30 * q^97 - 49 * q^98

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/855\mathbb{Z}\right)^\times$$.

 $$n$$ $$172$$ $$191$$ $$496$$ $$\chi(n)$$ $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$

## Coefficient data

For each $$n$$ we display the coefficients of the $$q$$-expansion $$a_n$$, the Satake parameters $$\alpha_p$$, and the Satake angles $$\theta_p = \textrm{Arg}(\alpha_p)$$.

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.898236 + 1.55579i −0.635149 + 1.10011i 0.351335 + 0.936250i $$0.385728\pi$$
−0.986484 + 0.163860i $$0.947605\pi$$
$$3$$ 0 0
$$4$$ −0.613656 1.06288i −0.306828 0.531442i
$$5$$ −0.500000 + 0.866025i −0.223607 + 0.387298i
$$6$$ 0 0
$$7$$ −3.41478 −1.29066 −0.645332 0.763902i $$-0.723281\pi$$
−0.645332 + 0.763902i $$0.723281\pi$$
$$8$$ −1.38811 −0.490771
$$9$$ 0 0
$$10$$ −0.898236 1.55579i −0.284047 0.491984i
$$11$$ 4.35669 1.31359 0.656796 0.754069i $$-0.271911\pi$$
0.656796 + 0.754069i $$0.271911\pi$$
$$12$$ 0 0
$$13$$ −2.49135 4.31514i −0.690976 1.19680i −0.971519 0.236963i $$-0.923848\pi$$
0.280543 0.959841i $$-0.409485\pi$$
$$14$$ 3.06728 5.31268i 0.819764 1.41987i
$$15$$ 0 0
$$16$$ 2.47416 4.28538i 0.618541 1.07134i
$$17$$ −0.0290433 + 0.0503046i −0.00704405 + 0.0122006i −0.869526 0.493887i $$-0.835576\pi$$
0.862482 + 0.506088i $$0.168909\pi$$
$$18$$ 0 0
$$19$$ −1.10304 4.21703i −0.253054 0.967452i
$$20$$ 1.22731 0.274435
$$21$$ 0 0
$$22$$ −3.91334 + 6.77810i −0.834326 + 1.44510i
$$23$$ 0.216041 + 0.374194i 0.0450476 + 0.0780247i 0.887670 0.460480i $$-0.152323\pi$$
−0.842622 + 0.538505i $$0.818989\pi$$
$$24$$ 0 0
$$25$$ −0.500000 0.866025i −0.100000 0.173205i
$$26$$ 8.95127 1.75549
$$27$$ 0 0
$$28$$ 2.09550 + 3.62951i 0.396012 + 0.685913i
$$29$$ 2.74750 + 4.75882i 0.510199 + 0.883690i 0.999930 + 0.0118169i $$0.00376151\pi$$
−0.489731 + 0.871873i $$0.662905\pi$$
$$30$$ 0 0
$$31$$ −0.592945 −0.106496 −0.0532480 0.998581i $$-0.516957\pi$$
−0.0532480 + 0.998581i $$0.516957\pi$$
$$32$$ 3.05666 + 5.29428i 0.540346 + 0.935906i
$$33$$ 0 0
$$34$$ −0.0521756 0.0903707i −0.00894804 0.0154985i
$$35$$ 1.70739 2.95728i 0.288601 0.499872i
$$36$$ 0 0
$$37$$ 6.62060 1.08842 0.544210 0.838949i $$-0.316830\pi$$
0.544210 + 0.838949i $$0.316830\pi$$
$$38$$ 7.55160 + 2.07179i 1.22503 + 0.336089i
$$39$$ 0 0
$$40$$ 0.694056 1.20214i 0.109740 0.190075i
$$41$$ 0.0818718 0.141806i 0.0127862 0.0221464i −0.859561 0.511032i $$-0.829263\pi$$
0.872348 + 0.488886i $$0.162597\pi$$
$$42$$ 0 0
$$43$$ 3.00242 5.20034i 0.457865 0.793045i −0.540983 0.841033i $$-0.681948\pi$$
0.998848 + 0.0479883i $$0.0152810\pi$$
$$44$$ −2.67351 4.63066i −0.403047 0.698098i
$$45$$ 0 0
$$46$$ −0.776222 −0.114448
$$47$$ −5.54529 9.60473i −0.808864 1.40099i −0.913651 0.406499i $$-0.866750\pi$$
0.104788 0.994495i $$-0.466584\pi$$
$$48$$ 0 0
$$49$$ 4.66070 0.665814
$$50$$ 1.79647 0.254060
$$51$$ 0 0
$$52$$ −3.05766 + 5.29603i −0.424022 + 0.734427i
$$53$$ −2.69971 4.67603i −0.370834 0.642303i 0.618860 0.785501i $$-0.287595\pi$$
−0.989694 + 0.143198i $$0.954261\pi$$
$$54$$ 0 0
$$55$$ −2.17835 + 3.77300i −0.293728 + 0.508752i
$$56$$ 4.74009 0.633421
$$57$$ 0 0
$$58$$ −9.87163 −1.29621
$$59$$ −1.72248 + 2.98342i −0.224248 + 0.388408i −0.956093 0.293062i $$-0.905326\pi$$
0.731846 + 0.681470i $$0.238659\pi$$
$$60$$ 0 0
$$61$$ −2.15698 3.73600i −0.276173 0.478346i 0.694257 0.719727i $$-0.255733\pi$$
−0.970430 + 0.241381i $$0.922400\pi$$
$$62$$ 0.532604 0.922498i 0.0676408 0.117157i
$$63$$ 0 0
$$64$$ −1.08574 −0.135718
$$65$$ 4.98270 0.618027
$$66$$ 0 0
$$67$$ 3.39217 + 5.87541i 0.414420 + 0.717796i 0.995367 0.0961450i $$-0.0306513\pi$$
−0.580948 + 0.813941i $$0.697318\pi$$
$$68$$ 0.0712905 0.00864525
$$69$$ 0 0
$$70$$ 3.06728 + 5.31268i 0.366610 + 0.634986i
$$71$$ 4.20501 7.28329i 0.499043 0.864368i −0.500956 0.865472i $$-0.667018\pi$$
0.999999 + 0.00110477i $$0.000351659\pi$$
$$72$$ 0 0
$$73$$ 5.84804 10.1291i 0.684461 1.18552i −0.289145 0.957285i $$-0.593371\pi$$
0.973606 0.228236i $$-0.0732958\pi$$
$$74$$ −5.94686 + 10.3003i −0.691309 + 1.19738i
$$75$$ 0 0
$$76$$ −3.80532 + 3.76021i −0.436501 + 0.431325i
$$77$$ −14.8771 −1.69541
$$78$$ 0 0
$$79$$ −3.64303 + 6.30991i −0.409873 + 0.709920i −0.994875 0.101111i $$-0.967760\pi$$
0.585003 + 0.811031i $$0.301094\pi$$
$$80$$ 2.47416 + 4.28538i 0.276620 + 0.479120i
$$81$$ 0 0
$$82$$ 0.147080 + 0.254751i 0.0162423 + 0.0281325i
$$83$$ 16.1185 1.76923 0.884617 0.466318i $$-0.154420\pi$$
0.884617 + 0.466318i $$0.154420\pi$$
$$84$$ 0 0
$$85$$ −0.0290433 0.0503046i −0.00315019 0.00545629i
$$86$$ 5.39377 + 9.34228i 0.581625 + 1.00740i
$$87$$ 0 0
$$88$$ −6.04757 −0.644673
$$89$$ −5.59024 9.68258i −0.592564 1.02635i −0.993886 0.110414i $$-0.964782\pi$$
0.401321 0.915937i $$-0.368551\pi$$
$$90$$ 0 0
$$91$$ 8.50740 + 14.7352i 0.891817 + 1.54467i
$$92$$ 0.265150 0.459252i 0.0276438 0.0478804i
$$93$$ 0 0
$$94$$ 19.9239 2.05500
$$95$$ 4.20357 + 1.15325i 0.431277 + 0.118321i
$$96$$ 0 0
$$97$$ −4.47355 + 7.74842i −0.454221 + 0.786733i −0.998643 0.0520780i $$-0.983416\pi$$
0.544422 + 0.838811i $$0.316749\pi$$
$$98$$ −4.18641 + 7.25107i −0.422891 + 0.732469i
$$99$$ 0 0
$$100$$ −0.613656 + 1.06288i −0.0613656 + 0.106288i
$$101$$ 1.09523 + 1.89700i 0.108980 + 0.188758i 0.915357 0.402643i $$-0.131908\pi$$
−0.806377 + 0.591401i $$0.798575\pi$$
$$102$$ 0 0
$$103$$ 10.4903 1.03364 0.516818 0.856095i $$-0.327117\pi$$
0.516818 + 0.856095i $$0.327117\pi$$
$$104$$ 3.45827 + 5.98990i 0.339111 + 0.587358i
$$105$$ 0 0
$$106$$ 9.69991 0.942138
$$107$$ −13.6911 −1.32357 −0.661783 0.749696i $$-0.730200\pi$$
−0.661783 + 0.749696i $$0.730200\pi$$
$$108$$ 0 0
$$109$$ 7.07679 12.2574i 0.677834 1.17404i −0.297798 0.954629i $$-0.596252\pi$$
0.975632 0.219413i $$-0.0704144\pi$$
$$110$$ −3.91334 6.77810i −0.373122 0.646266i
$$111$$ 0 0
$$112$$ −8.44872 + 14.6336i −0.798329 + 1.38275i
$$113$$ −13.2851 −1.24976 −0.624879 0.780722i $$-0.714852\pi$$
−0.624879 + 0.780722i $$0.714852\pi$$
$$114$$ 0 0
$$115$$ −0.432081 −0.0402918
$$116$$ 3.37205 5.84056i 0.313087 0.542282i
$$117$$ 0 0
$$118$$ −3.09438 5.35963i −0.284861 0.493394i
$$119$$ 0.0991765 0.171779i 0.00909150 0.0157469i
$$120$$ 0 0
$$121$$ 7.98075 0.725523
$$122$$ 7.74991 0.701644
$$123$$ 0 0
$$124$$ 0.363864 + 0.630231i 0.0326760 + 0.0565964i
$$125$$ 1.00000 0.0894427
$$126$$ 0 0
$$127$$ −7.84813 13.5934i −0.696409 1.20622i −0.969703 0.244285i $$-0.921447\pi$$
0.273295 0.961930i $$-0.411887\pi$$
$$128$$ −5.13806 + 8.89938i −0.454145 + 0.786602i
$$129$$ 0 0
$$130$$ −4.47564 + 7.75203i −0.392539 + 0.679898i
$$131$$ 5.86776 10.1633i 0.512669 0.887968i −0.487223 0.873277i $$-0.661990\pi$$
0.999892 0.0146910i $$-0.00467646\pi$$
$$132$$ 0 0
$$133$$ 3.76663 + 14.4002i 0.326608 + 1.24866i
$$134$$ −12.1879 −1.05287
$$135$$ 0 0
$$136$$ 0.0403154 0.0698283i 0.00345702 0.00598773i
$$137$$ 5.12860 + 8.88300i 0.438166 + 0.758926i 0.997548 0.0699840i $$-0.0222948\pi$$
−0.559382 + 0.828910i $$0.688962\pi$$
$$138$$ 0 0
$$139$$ −10.9044 18.8870i −0.924899 1.60197i −0.791723 0.610880i $$-0.790816\pi$$
−0.133176 0.991092i $$-0.542518\pi$$
$$140$$ −4.19100 −0.354204
$$141$$ 0 0
$$142$$ 7.55418 + 13.0842i 0.633933 + 1.09800i
$$143$$ −10.8540 18.7997i −0.907660 1.57211i
$$144$$ 0 0
$$145$$ −5.49501 −0.456336
$$146$$ 10.5058 + 18.1966i 0.869469 + 1.50597i
$$147$$ 0 0
$$148$$ −4.06277 7.03693i −0.333958 0.578432i
$$149$$ −10.3765 + 17.9727i −0.850079 + 1.47238i 0.0310582 + 0.999518i $$0.490112\pi$$
−0.881137 + 0.472862i $$0.843221\pi$$
$$150$$ 0 0
$$151$$ −14.9510 −1.21669 −0.608346 0.793672i $$-0.708167\pi$$
−0.608346 + 0.793672i $$0.708167\pi$$
$$152$$ 1.53114 + 5.85370i 0.124192 + 0.474798i
$$153$$ 0 0
$$154$$ 13.3632 23.1457i 1.07683 1.86513i
$$155$$ 0.296472 0.513505i 0.0238132 0.0412457i
$$156$$ 0 0
$$157$$ 0.0399391 0.0691765i 0.00318749 0.00552089i −0.864427 0.502758i $$-0.832319\pi$$
0.867615 + 0.497237i $$0.165652\pi$$
$$158$$ −6.54460 11.3356i −0.520660 0.901810i
$$159$$ 0 0
$$160$$ −6.11331 −0.483300
$$161$$ −0.737731 1.27779i −0.0581413 0.100704i
$$162$$ 0 0
$$163$$ 18.4845 1.44782 0.723909 0.689896i $$-0.242344\pi$$
0.723909 + 0.689896i $$0.242344\pi$$
$$164$$ −0.200965 −0.0156927
$$165$$ 0 0
$$166$$ −14.4782 + 25.0770i −1.12373 + 1.94635i
$$167$$ −9.34180 16.1805i −0.722890 1.25208i −0.959837 0.280560i $$-0.909480\pi$$
0.236946 0.971523i $$-0.423853\pi$$
$$168$$ 0 0
$$169$$ −5.91363 + 10.2427i −0.454894 + 0.787900i
$$170$$ 0.104351 0.00800337
$$171$$ 0 0
$$172$$ −7.36982 −0.561943
$$173$$ −4.29860 + 7.44540i −0.326817 + 0.566063i −0.981878 0.189512i $$-0.939309\pi$$
0.655062 + 0.755575i $$0.272643\pi$$
$$174$$ 0 0
$$175$$ 1.70739 + 2.95728i 0.129066 + 0.223550i
$$176$$ 10.7792 18.6701i 0.812510 1.40731i
$$177$$ 0 0
$$178$$ 20.0854 1.50547
$$179$$ 6.16587 0.460859 0.230429 0.973089i $$-0.425987\pi$$
0.230429 + 0.973089i $$0.425987\pi$$
$$180$$ 0 0
$$181$$ −10.0294 17.3715i −0.745481 1.29121i −0.949970 0.312343i $$-0.898886\pi$$
0.204488 0.978869i $$-0.434447\pi$$
$$182$$ −30.5666 −2.26575
$$183$$ 0 0
$$184$$ −0.299889 0.519422i −0.0221081 0.0382923i
$$185$$ −3.31030 + 5.73361i −0.243378 + 0.421543i
$$186$$ 0 0
$$187$$ −0.126533 + 0.219161i −0.00925300 + 0.0160267i
$$188$$ −6.80581 + 11.7880i −0.496364 + 0.859728i
$$189$$ 0 0
$$190$$ −5.57002 + 5.50398i −0.404092 + 0.399301i
$$191$$ −17.0701 −1.23515 −0.617573 0.786513i $$-0.711884\pi$$
−0.617573 + 0.786513i $$0.711884\pi$$
$$192$$ 0 0
$$193$$ −3.63576 + 6.29733i −0.261708 + 0.453292i −0.966696 0.255928i $$-0.917619\pi$$
0.704988 + 0.709219i $$0.250952\pi$$
$$194$$ −8.03662 13.9198i −0.576995 0.999385i
$$195$$ 0 0
$$196$$ −2.86007 4.95378i −0.204291 0.353842i
$$197$$ −3.59854 −0.256385 −0.128193 0.991749i $$-0.540918\pi$$
−0.128193 + 0.991749i $$0.540918\pi$$
$$198$$ 0 0
$$199$$ −10.7918 18.6919i −0.765008 1.32503i −0.940242 0.340506i $$-0.889402\pi$$
0.175234 0.984527i $$-0.443932\pi$$
$$200$$ 0.694056 + 1.20214i 0.0490771 + 0.0850041i
$$201$$ 0 0
$$202$$ −3.93511 −0.276873
$$203$$ −9.38211 16.2503i −0.658495 1.14055i
$$204$$ 0 0
$$205$$ 0.0818718 + 0.141806i 0.00571817 + 0.00990417i
$$206$$ −9.42272 + 16.3206i −0.656512 + 1.13711i
$$207$$ 0 0
$$208$$ −24.6560 −1.70959
$$209$$ −4.80559 18.3723i −0.332410 1.27084i
$$210$$ 0 0
$$211$$ −0.0351916 + 0.0609536i −0.00242269 + 0.00419622i −0.867234 0.497900i $$-0.834105\pi$$
0.864812 + 0.502097i $$0.167438\pi$$
$$212$$ −3.31339 + 5.73896i −0.227564 + 0.394153i
$$213$$ 0 0
$$214$$ 12.2978 21.3004i 0.840661 1.45607i
$$215$$ 3.00242 + 5.20034i 0.204763 + 0.354661i
$$216$$ 0 0
$$217$$ 2.02477 0.137451
$$218$$ 12.7133 + 22.0200i 0.861051 + 1.49138i
$$219$$ 0 0
$$220$$ 5.34702 0.360496
$$221$$ 0.289428 0.0194691
$$222$$ 0 0
$$223$$ 6.52703 11.3051i 0.437082 0.757049i −0.560381 0.828235i $$-0.689345\pi$$
0.997463 + 0.0711864i $$0.0226785\pi$$
$$224$$ −10.4378 18.0788i −0.697405 1.20794i
$$225$$ 0 0
$$226$$ 11.9332 20.6689i 0.793783 1.37487i
$$227$$ 7.75546 0.514748 0.257374 0.966312i $$-0.417143\pi$$
0.257374 + 0.966312i $$0.417143\pi$$
$$228$$ 0 0
$$229$$ 19.0597 1.25950 0.629751 0.776797i $$-0.283157\pi$$
0.629751 + 0.776797i $$0.283157\pi$$
$$230$$ 0.388111 0.672228i 0.0255913 0.0443254i
$$231$$ 0 0
$$232$$ −3.81384 6.60577i −0.250391 0.433690i
$$233$$ 6.26723 10.8552i 0.410580 0.711145i −0.584373 0.811485i $$-0.698660\pi$$
0.994953 + 0.100340i $$0.0319930\pi$$
$$234$$ 0 0
$$235$$ 11.0906 0.723470
$$236$$ 4.22804 0.275222
$$237$$ 0 0
$$238$$ 0.178168 + 0.308596i 0.0115489 + 0.0200033i
$$239$$ 15.7879 1.02123 0.510617 0.859808i $$-0.329417\pi$$
0.510617 + 0.859808i $$0.329417\pi$$
$$240$$ 0 0
$$241$$ −12.4166 21.5061i −0.799822 1.38533i −0.919732 0.392547i $$-0.871594\pi$$
0.119910 0.992785i $$-0.461739\pi$$
$$242$$ −7.16860 + 12.4164i −0.460815 + 0.798155i
$$243$$ 0 0
$$244$$ −2.64729 + 4.58524i −0.169475 + 0.293540i
$$245$$ −2.33035 + 4.03628i −0.148881 + 0.257869i
$$246$$ 0 0
$$247$$ −15.4490 + 15.2658i −0.982997 + 0.971342i
$$248$$ 0.823073 0.0522652
$$249$$ 0 0
$$250$$ −0.898236 + 1.55579i −0.0568094 + 0.0983968i
$$251$$ −1.65676 2.86958i −0.104573 0.181127i 0.808990 0.587822i $$-0.200014\pi$$
−0.913564 + 0.406695i $$0.866681\pi$$
$$252$$ 0 0
$$253$$ 0.941223 + 1.63025i 0.0591742 + 0.102493i
$$254$$ 28.1979 1.76929
$$255$$ 0 0
$$256$$ −10.3161 17.8681i −0.644758 1.11675i
$$257$$ 12.4325 + 21.5337i 0.775516 + 1.34323i 0.934504 + 0.355952i $$0.115843\pi$$
−0.158988 + 0.987280i $$0.550823\pi$$
$$258$$ 0 0
$$259$$ −22.6079 −1.40478
$$260$$ −3.05766 5.29603i −0.189628 0.328446i
$$261$$ 0 0
$$262$$ 10.5413 + 18.2580i 0.651242 + 1.12798i
$$263$$ 0.342686 0.593549i 0.0211309 0.0365998i −0.855267 0.518188i $$-0.826607\pi$$
0.876397 + 0.481588i $$0.159940\pi$$
$$264$$ 0 0
$$265$$ 5.39942 0.331684
$$266$$ −25.7870 7.07470i −1.58110 0.433778i
$$267$$ 0 0
$$268$$ 4.16325 7.21097i 0.254311 0.440480i
$$269$$ −5.58704 + 9.67704i −0.340648 + 0.590019i −0.984553 0.175086i $$-0.943980\pi$$
0.643905 + 0.765105i $$0.277313\pi$$
$$270$$ 0 0
$$271$$ 7.16308 12.4068i 0.435126 0.753661i −0.562180 0.827015i $$-0.690037\pi$$
0.997306 + 0.0733542i $$0.0233704\pi$$
$$272$$ 0.143716 + 0.248923i 0.00871406 + 0.0150932i
$$273$$ 0 0
$$274$$ −18.4268 −1.11320
$$275$$ −2.17835 3.77300i −0.131359 0.227521i
$$276$$ 0 0
$$277$$ −15.3518 −0.922397 −0.461199 0.887297i $$-0.652580\pi$$
−0.461199 + 0.887297i $$0.652580\pi$$
$$278$$ 39.1789 2.34979
$$279$$ 0 0
$$280$$ −2.37004 + 4.10504i −0.141637 + 0.245323i
$$281$$ −4.80640 8.32493i −0.286726 0.496624i 0.686300 0.727318i $$-0.259234\pi$$
−0.973026 + 0.230694i $$0.925900\pi$$
$$282$$ 0 0
$$283$$ −2.86255 + 4.95809i −0.170161 + 0.294728i −0.938476 0.345344i $$-0.887762\pi$$
0.768315 + 0.640072i $$0.221095\pi$$
$$284$$ −10.3217 −0.612482
$$285$$ 0 0
$$286$$ 38.9979 2.30600
$$287$$ −0.279574 + 0.484236i −0.0165027 + 0.0285836i
$$288$$ 0 0
$$289$$ 8.49831 + 14.7195i 0.499901 + 0.865854i
$$290$$ 4.93582 8.54908i 0.289841 0.502019i
$$291$$ 0 0
$$292$$ −14.3547 −0.840048
$$293$$ −23.3141 −1.36203 −0.681013 0.732271i $$-0.738460\pi$$
−0.681013 + 0.732271i $$0.738460\pi$$
$$294$$ 0 0
$$295$$ −1.72248 2.98342i −0.100287 0.173701i
$$296$$ −9.19013 −0.534165
$$297$$ 0 0
$$298$$ −18.6412 32.2874i −1.07985 1.87036i
$$299$$ 1.07647 1.86449i 0.0622536 0.107826i
$$300$$ 0 0
$$301$$ −10.2526 + 17.7580i −0.590950 + 1.02356i
$$302$$ 13.4295 23.2606i 0.772781 1.33850i
$$303$$ 0 0
$$304$$ −20.8006 5.70668i −1.19300 0.327301i
$$305$$ 4.31396 0.247017
$$306$$ 0 0
$$307$$ −4.24686 + 7.35577i −0.242381 + 0.419816i −0.961392 0.275183i $$-0.911262\pi$$
0.719011 + 0.694999i $$0.244595\pi$$
$$308$$ 9.12944 + 15.8127i 0.520198 + 0.901010i
$$309$$ 0 0
$$310$$ 0.532604 + 0.922498i 0.0302499 + 0.0523943i
$$311$$ −4.54326 −0.257625 −0.128812 0.991669i $$-0.541116\pi$$
−0.128812 + 0.991669i $$0.541116\pi$$
$$312$$ 0 0
$$313$$ 9.43148 + 16.3358i 0.533099 + 0.923354i 0.999253 + 0.0386503i $$0.0123058\pi$$
−0.466154 + 0.884703i $$0.654361\pi$$
$$314$$ 0.0717495 + 0.124274i 0.00404906 + 0.00701317i
$$315$$ 0 0
$$316$$ 8.94227 0.503042
$$317$$ 9.61822 + 16.6592i 0.540213 + 0.935677i 0.998891 + 0.0470741i $$0.0149897\pi$$
−0.458678 + 0.888602i $$0.651677\pi$$
$$318$$ 0 0
$$319$$ 11.9700 + 20.7327i 0.670193 + 1.16081i
$$320$$ 0.542870 0.940279i 0.0303474 0.0525632i
$$321$$ 0 0
$$322$$ 2.65063 0.147714
$$323$$ 0.244172 + 0.0669888i 0.0135861 + 0.00372735i
$$324$$ 0 0
$$325$$ −2.49135 + 4.31514i −0.138195 + 0.239361i
$$326$$ −16.6034 + 28.7580i −0.919579 + 1.59276i
$$327$$ 0 0
$$328$$ −0.113647 + 0.196843i −0.00627511 + 0.0108688i
$$329$$ 18.9359 + 32.7980i 1.04397 + 1.80821i
$$330$$ 0 0
$$331$$ 9.49306 0.521786 0.260893 0.965368i $$-0.415983\pi$$
0.260893 + 0.965368i $$0.415983\pi$$
$$332$$ −9.89121 17.1321i −0.542851 0.940245i
$$333$$ 0 0
$$334$$ 33.5646 1.83657
$$335$$ −6.78434 −0.370668
$$336$$ 0 0
$$337$$ −11.8854 + 20.5860i −0.647437 + 1.12139i 0.336296 + 0.941756i $$0.390826\pi$$
−0.983733 + 0.179637i $$0.942508\pi$$
$$338$$ −10.6237 18.4007i −0.577851 1.00087i
$$339$$ 0 0
$$340$$ −0.0356453 + 0.0617394i −0.00193314 + 0.00334829i
$$341$$ −2.58328 −0.139892
$$342$$ 0 0
$$343$$ 7.98819 0.431322
$$344$$ −4.16769 + 7.21866i −0.224707 + 0.389204i
$$345$$ 0 0
$$346$$ −7.72232 13.3755i −0.415155 0.719069i
$$347$$ 14.0069 24.2607i 0.751932 1.30238i −0.194953 0.980813i $$-0.562455\pi$$
0.946885 0.321572i $$-0.104211\pi$$
$$348$$ 0 0
$$349$$ 0.00959659 0.000513694 0.000256847 1.00000i $$-0.499918\pi$$
0.000256847 1.00000i $$0.499918\pi$$
$$350$$ −6.13455 −0.327906
$$351$$ 0 0
$$352$$ 13.3169 + 23.0656i 0.709793 + 1.22940i
$$353$$ −6.08582 −0.323915 −0.161958 0.986798i $$-0.551781\pi$$
−0.161958 + 0.986798i $$0.551781\pi$$
$$354$$ 0 0
$$355$$ 4.20501 + 7.28329i 0.223179 + 0.386557i
$$356$$ −6.86097 + 11.8836i −0.363631 + 0.629827i
$$357$$ 0 0
$$358$$ −5.53841 + 9.59281i −0.292714 + 0.506996i
$$359$$ −8.91042 + 15.4333i −0.470274 + 0.814538i −0.999422 0.0339910i $$-0.989178\pi$$
0.529148 + 0.848529i $$0.322512\pi$$
$$360$$ 0 0
$$361$$ −16.5666 + 9.30307i −0.871927 + 0.489635i
$$362$$ 36.0352 1.89397
$$363$$ 0 0
$$364$$ 10.4412 18.0848i 0.547269 0.947898i
$$365$$ 5.84804 + 10.1291i 0.306100 + 0.530181i
$$366$$ 0 0
$$367$$ 2.45095 + 4.24517i 0.127938 + 0.221596i 0.922878 0.385093i $$-0.125831\pi$$
−0.794939 + 0.606689i $$0.792497\pi$$
$$368$$ 2.13808 0.111455
$$369$$ 0 0
$$370$$ −5.94686 10.3003i −0.309163 0.535485i
$$371$$ 9.21891 + 15.9676i 0.478622 + 0.828997i
$$372$$ 0 0
$$373$$ −12.9995 −0.673090 −0.336545 0.941667i $$-0.609258\pi$$
−0.336545 + 0.941667i $$0.609258\pi$$
$$374$$ −0.227313 0.393717i −0.0117541 0.0203586i
$$375$$ 0 0
$$376$$ 7.69748 + 13.3324i 0.396967 + 0.687567i
$$377$$ 13.6900 23.7117i 0.705070 1.22122i
$$378$$ 0 0
$$379$$ 16.7313 0.859427 0.429713 0.902965i $$-0.358615\pi$$
0.429713 + 0.902965i $$0.358615\pi$$
$$380$$ −1.35377 5.17561i −0.0694470 0.265503i
$$381$$ 0 0
$$382$$ 15.3330 26.5575i 0.784502 1.35880i
$$383$$ −14.9461 + 25.8875i −0.763712 + 1.32279i 0.177213 + 0.984172i $$0.443292\pi$$
−0.940925 + 0.338615i $$0.890042\pi$$
$$384$$ 0 0
$$385$$ 7.43856 12.8840i 0.379104 0.656628i
$$386$$ −6.53155 11.3130i −0.332447 0.575815i
$$387$$ 0 0
$$388$$ 10.9809 0.557471
$$389$$ −15.8669 27.4822i −0.804483 1.39340i −0.916640 0.399714i $$-0.869109\pi$$
0.112157 0.993691i $$-0.464224\pi$$
$$390$$ 0 0
$$391$$ −0.0250982 −0.00126927
$$392$$ −6.46957 −0.326763
$$393$$ 0 0
$$394$$ 3.23234 5.59857i 0.162843 0.282052i
$$395$$ −3.64303 6.30991i −0.183301 0.317486i
$$396$$ 0 0
$$397$$ −16.9999 + 29.4447i −0.853202 + 1.47779i 0.0251017 + 0.999685i $$0.492009\pi$$
−0.878303 + 0.478104i $$0.841324\pi$$
$$398$$ 38.7742 1.94358
$$399$$ 0 0
$$400$$ −4.94833 −0.247416
$$401$$ 4.55045 7.88161i 0.227239 0.393589i −0.729750 0.683714i $$-0.760364\pi$$
0.956989 + 0.290125i $$0.0936970\pi$$
$$402$$ 0 0
$$403$$ 1.47723 + 2.55864i 0.0735861 + 0.127455i
$$404$$ 1.34419 2.32821i 0.0668761 0.115833i
$$405$$ 0 0
$$406$$ 33.7094 1.67297
$$407$$ 28.8439 1.42974
$$408$$ 0 0
$$409$$ 13.9425 + 24.1491i 0.689411 + 1.19409i 0.972029 + 0.234862i $$0.0754639\pi$$
−0.282618 + 0.959233i $$0.591203\pi$$
$$410$$ −0.294161 −0.0145276
$$411$$ 0 0
$$412$$ −6.43741 11.1499i −0.317148 0.549317i
$$413$$ 5.88188 10.1877i 0.289428 0.501305i
$$414$$ 0 0
$$415$$ −8.05924 + 13.9590i −0.395613 + 0.685221i
$$416$$ 15.2304 26.3798i 0.746731 1.29338i
$$417$$ 0 0
$$418$$ 32.9000 + 9.02615i 1.60919 + 0.441483i
$$419$$ 31.5961 1.54357 0.771785 0.635884i $$-0.219364\pi$$
0.771785 + 0.635884i $$0.219364\pi$$
$$420$$ 0 0
$$421$$ −6.42177 + 11.1228i −0.312978 + 0.542094i −0.979006 0.203833i $$-0.934660\pi$$
0.666028 + 0.745927i $$0.267993\pi$$
$$422$$ −0.0632207 0.109502i −0.00307754 0.00533045i
$$423$$ 0 0
$$424$$ 3.74750 + 6.49086i 0.181995 + 0.315224i
$$425$$ 0.0580867 0.00281762
$$426$$ 0 0
$$427$$ 7.36561 + 12.7576i 0.356447 + 0.617384i
$$428$$ 8.40161 + 14.5520i 0.406107 + 0.703398i
$$429$$ 0 0
$$430$$ −10.7875 −0.520221
$$431$$ −16.6064 28.7630i −0.799900 1.38547i −0.919681 0.392667i $$-0.871553\pi$$
0.119781 0.992800i $$-0.461781\pi$$
$$432$$ 0 0
$$433$$ −3.66146 6.34183i −0.175958 0.304769i 0.764534 0.644583i $$-0.222969\pi$$
−0.940493 + 0.339814i $$0.889636\pi$$
$$434$$ −1.81872 + 3.15012i −0.0873016 + 0.151211i
$$435$$ 0 0
$$436$$ −17.3709 −0.831914
$$437$$ 1.33968 1.32380i 0.0640857 0.0633259i
$$438$$ 0 0
$$439$$ −11.4327 + 19.8020i −0.545651 + 0.945096i 0.452914 + 0.891554i $$0.350384\pi$$
−0.998566 + 0.0535417i $$0.982949\pi$$
$$440$$ 3.02379 5.23735i 0.144153 0.249681i
$$441$$ 0 0
$$442$$ −0.259975 + 0.450290i −0.0123657 + 0.0214181i
$$443$$ −7.40824 12.8315i −0.351976 0.609641i 0.634619 0.772825i $$-0.281157\pi$$
−0.986596 + 0.163184i $$0.947824\pi$$
$$444$$ 0 0
$$445$$ 11.1805 0.530006
$$446$$ 11.7256 + 20.3094i 0.555225 + 0.961677i
$$447$$ 0 0
$$448$$ 3.70756 0.175166
$$449$$ 41.8708 1.97600 0.988002 0.154441i $$-0.0493576\pi$$
0.988002 + 0.154441i $$0.0493576\pi$$
$$450$$ 0 0
$$451$$ 0.356690 0.617805i 0.0167959 0.0290913i
$$452$$ 8.15249 + 14.1205i 0.383461 + 0.664174i
$$453$$ 0 0
$$454$$ −6.96623 + 12.0659i −0.326942 + 0.566279i
$$455$$ −17.0148 −0.797666
$$456$$ 0 0
$$457$$ 38.4845 1.80023 0.900114 0.435655i $$-0.143483\pi$$
0.900114 + 0.435655i $$0.143483\pi$$
$$458$$ −17.1201 + 29.6530i −0.799972 + 1.38559i
$$459$$ 0 0
$$460$$ 0.265150 + 0.459252i 0.0123627 + 0.0214128i
$$461$$ −13.9830 + 24.2192i −0.651251 + 1.12800i 0.331568 + 0.943431i $$0.392422\pi$$
−0.982820 + 0.184569i $$0.940911\pi$$
$$462$$ 0 0
$$463$$ 12.5403 0.582797 0.291399 0.956602i $$-0.405879\pi$$
0.291399 + 0.956602i $$0.405879\pi$$
$$464$$ 27.1911 1.26232
$$465$$ 0 0
$$466$$ 11.2589 + 19.5010i 0.521559 + 0.903366i
$$467$$ 24.4525 1.13153 0.565764 0.824567i $$-0.308581\pi$$
0.565764 + 0.824567i $$0.308581\pi$$
$$468$$ 0 0
$$469$$ −11.5835 20.0632i −0.534877 0.926434i
$$470$$ −9.96196 + 17.2546i −0.459511 + 0.795896i
$$471$$ 0 0
$$472$$ 2.39099 4.14132i 0.110054 0.190620i
$$473$$ 13.0806 22.6563i 0.601447 1.04174i
$$474$$ 0 0
$$475$$ −3.10053 + 3.06377i −0.142262 + 0.140575i
$$476$$ −0.243441 −0.0111581
$$477$$ 0 0
$$478$$ −14.1813 + 24.5626i −0.648635 + 1.12347i
$$479$$ 3.27876 + 5.67898i 0.149810 + 0.259479i 0.931157 0.364618i $$-0.118800\pi$$
−0.781347 + 0.624097i $$0.785467\pi$$
$$480$$ 0 0
$$481$$ −16.4942 28.5688i −0.752071 1.30263i
$$482$$ 44.6121 2.03202
$$483$$ 0 0
$$484$$ −4.89744 8.48261i −0.222611 0.385573i
$$485$$ −4.47355 7.74842i −0.203134 0.351838i
$$486$$ 0 0
$$487$$ −12.6305 −0.572341 −0.286170 0.958179i $$-0.592382\pi$$
−0.286170 + 0.958179i $$0.592382\pi$$
$$488$$ 2.99413 + 5.18598i 0.135538 + 0.234758i
$$489$$ 0 0
$$490$$ −4.18641 7.25107i −0.189123 0.327570i
$$491$$ 6.46604 11.1995i 0.291808 0.505427i −0.682429 0.730952i $$-0.739076\pi$$
0.974237 + 0.225525i $$0.0724098\pi$$
$$492$$ 0 0
$$493$$ −0.319187 −0.0143755
$$494$$ −9.87359 37.7478i −0.444234 1.69835i
$$495$$ 0 0
$$496$$ −1.46704 + 2.54099i −0.0658722 + 0.114094i
$$497$$ −14.3592 + 24.8708i −0.644097 + 1.11561i
$$498$$ 0 0
$$499$$ 14.9627 25.9162i 0.669824 1.16017i −0.308129 0.951345i $$-0.599703\pi$$
0.977953 0.208825i $$-0.0669639\pi$$
$$500$$ −0.613656 1.06288i −0.0274435 0.0475336i
$$501$$ 0 0
$$502$$ 5.95263 0.265679
$$503$$ −15.1592 26.2565i −0.675914 1.17072i −0.976201 0.216869i $$-0.930416\pi$$
0.300287 0.953849i $$-0.402918\pi$$
$$504$$ 0 0
$$505$$ −2.19046 −0.0974744
$$506$$ −3.38176 −0.150338
$$507$$ 0 0
$$508$$ −9.63211 + 16.6833i −0.427356 + 0.740202i
$$509$$ 13.2252 + 22.9067i 0.586197 + 1.01532i 0.994725 + 0.102577i $$0.0327088\pi$$
−0.408528 + 0.912746i $$0.633958\pi$$
$$510$$ 0 0
$$511$$ −19.9697 + 34.5886i −0.883409 + 1.53011i
$$512$$ 16.5130 0.729779
$$513$$ 0 0
$$514$$ −44.6692 −1.97027
$$515$$ −5.24513 + 9.08483i −0.231128 + 0.400325i
$$516$$ 0 0
$$517$$ −24.1591 41.8448i −1.06252 1.84033i
$$518$$ 20.3072 35.1731i 0.892247 1.54542i
$$519$$ 0 0
$$520$$ −6.91654 −0.303310
$$521$$ 3.32486 0.145665 0.0728324 0.997344i $$-0.476796\pi$$
0.0728324 + 0.997344i $$0.476796\pi$$
$$522$$ 0 0
$$523$$ −8.88844 15.3952i −0.388664 0.673186i 0.603606 0.797283i $$-0.293730\pi$$
−0.992270 + 0.124097i $$0.960397\pi$$
$$524$$ −14.4032 −0.629205
$$525$$ 0 0
$$526$$ 0.615626 + 1.06630i 0.0268426 + 0.0464927i
$$527$$ 0.0172211 0.0298278i 0.000750163 0.00129932i
$$528$$ 0 0
$$529$$ 11.4067 19.7569i 0.495941 0.858996i
$$530$$ −4.84995 + 8.40037i −0.210669 + 0.364889i
$$531$$ 0 0
$$532$$ 12.9943 12.8403i 0.563376 0.556696i
$$533$$ −0.815884 −0.0353399
$$534$$ 0 0
$$535$$ 6.84553 11.8568i 0.295958 0.512615i
$$536$$ −4.70871 8.15573i −0.203385 0.352274i
$$537$$ 0 0
$$538$$ −10.0370 17.3845i −0.432724 0.749500i
$$539$$ 20.3052 0.874608
$$540$$ 0 0
$$541$$ 17.7241 + 30.6991i 0.762021 + 1.31986i 0.941808 + 0.336153i $$0.109126\pi$$
−0.179787 + 0.983706i $$0.557541\pi$$
$$542$$ 12.8683 + 22.2885i 0.552740 + 0.957374i
$$543$$ 0 0
$$544$$ −0.355102 −0.0152249
$$545$$ 7.07679 + 12.2574i 0.303136 + 0.525048i
$$546$$ 0 0
$$547$$ −9.90142 17.1498i −0.423354 0.733271i 0.572911 0.819618i $$-0.305814\pi$$
−0.996265 + 0.0863465i $$0.972481\pi$$
$$548$$ 6.29440 10.9022i 0.268883 0.465720i
$$549$$ 0 0
$$550$$ 7.82667 0.333730
$$551$$ 17.0375 16.8355i 0.725820 0.717214i
$$552$$ 0 0
$$553$$ 12.4401 21.5469i 0.529008 0.916269i
$$554$$ 13.7895 23.8841i 0.585860 1.01474i
$$555$$ 0 0
$$556$$ −13.3831 + 23.1802i −0.567570 + 0.983061i
$$557$$ −13.6340 23.6148i −0.577692 1.00059i −0.995743 0.0921684i $$-0.970620\pi$$
0.418052 0.908423i $$-0.362713\pi$$
$$558$$ 0 0
$$559$$ −29.9203 −1.26549
$$560$$ −8.44872 14.6336i −0.357024 0.618383i
$$561$$ 0 0
$$562$$ 17.2691 0.728455
$$563$$ 28.6245 1.20638 0.603190 0.797598i $$-0.293896\pi$$
0.603190 + 0.797598i $$0.293896\pi$$
$$564$$ 0 0
$$565$$ 6.64256 11.5052i 0.279454 0.484029i
$$566$$ −5.14250 8.90706i −0.216155 0.374392i
$$567$$ 0 0
$$568$$ −5.83702 + 10.1100i −0.244916 + 0.424207i
$$569$$ −32.2230 −1.35086 −0.675430 0.737424i $$-0.736042\pi$$
−0.675430 + 0.737424i $$0.736042\pi$$
$$570$$ 0 0
$$571$$ −7.39249 −0.309366 −0.154683 0.987964i $$-0.549436\pi$$
−0.154683 + 0.987964i $$0.549436\pi$$
$$572$$ −13.3213 + 23.0731i −0.556991 + 0.964737i
$$573$$ 0 0
$$574$$ −0.502247 0.869917i −0.0209634 0.0363096i
$$575$$ 0.216041 0.374194i 0.00900952 0.0156049i
$$576$$ 0 0
$$577$$ 3.03682 0.126425 0.0632123 0.998000i $$-0.479865\pi$$
0.0632123 + 0.998000i $$0.479865\pi$$
$$578$$ −30.5340 −1.27005
$$579$$ 0 0
$$580$$ 3.37205 + 5.84056i 0.140017 + 0.242516i
$$581$$ −55.0410 −2.28349
$$582$$ 0 0
$$583$$ −11.7618 20.3720i −0.487124 0.843723i
$$584$$ −8.11773 + 14.0603i −0.335914 + 0.581820i
$$585$$ 0 0
$$586$$ 20.9416 36.2719i 0.865089 1.49838i
$$587$$ −7.96968 + 13.8039i −0.328944 + 0.569748i −0.982303 0.187301i $$-0.940026\pi$$
0.653359 + 0.757048i $$0.273359\pi$$
$$588$$ 0 0
$$589$$ 0.654040 + 2.50046i 0.0269492 + 0.103030i
$$590$$ 6.18877 0.254788
$$591$$ 0 0
$$592$$ 16.3804 28.3718i 0.673232 1.16607i
$$593$$ 13.2914 + 23.0213i 0.545811 + 0.945373i 0.998555 + 0.0537322i $$0.0171117\pi$$
−0.452744 + 0.891640i $$0.649555\pi$$
$$594$$ 0 0
$$595$$ 0.0991765 + 0.171779i 0.00406584 + 0.00704224i
$$596$$ 25.4705 1.04331
$$597$$ 0 0
$$598$$ 1.93384 + 3.34951i 0.0790806 + 0.136972i
$$599$$ 18.8742 + 32.6911i 0.771181 + 1.33572i 0.936916 + 0.349554i $$0.113667\pi$$
−0.165736 + 0.986170i $$0.553000\pi$$
$$600$$ 0 0
$$601$$ −16.9222 −0.690269 −0.345134 0.938553i $$-0.612167\pi$$
−0.345134 + 0.938553i $$0.612167\pi$$
$$602$$ −18.4185 31.9018i −0.750682 1.30022i
$$603$$ 0 0
$$604$$ 9.17476 + 15.8911i 0.373316 + 0.646601i
$$605$$ −3.99037 + 6.91153i −0.162232 + 0.280994i
$$606$$ 0 0
$$607$$ 36.3712 1.47626 0.738131 0.674658i $$-0.235709\pi$$
0.738131 + 0.674658i $$0.235709\pi$$
$$608$$ 18.9545 18.7298i 0.768708 0.759593i
$$609$$ 0 0
$$610$$ −3.87496 + 6.71162i −0.156892 + 0.271746i
$$611$$ −27.6305 + 47.8574i −1.11781 + 1.93610i
$$612$$ 0 0
$$613$$ −3.66105 + 6.34113i −0.147869 + 0.256116i −0.930439 0.366446i $$-0.880575\pi$$
0.782571 + 0.622561i $$0.213908\pi$$
$$614$$ −7.62936 13.2144i −0.307896 0.533291i
$$615$$ 0 0
$$616$$ 20.6511 0.832057
$$617$$ 4.91459 + 8.51233i 0.197854 + 0.342693i 0.947832 0.318769i $$-0.103269\pi$$
−0.749978 + 0.661462i $$0.769936\pi$$
$$618$$ 0 0
$$619$$ 8.29932 0.333578 0.166789 0.985993i $$-0.446660\pi$$
0.166789 + 0.985993i $$0.446660\pi$$
$$620$$ −0.727729 −0.0292263
$$621$$ 0 0
$$622$$ 4.08092 7.06836i 0.163630 0.283415i
$$623$$ 19.0894 + 33.0639i 0.764802 + 1.32468i
$$624$$ 0 0
$$625$$ −0.500000 + 0.866025i −0.0200000 + 0.0346410i
$$626$$ −33.8868 −1.35439
$$627$$ 0 0
$$628$$ −0.0980355 −0.00391204
$$629$$ −0.192284 + 0.333046i −0.00766688 + 0.0132794i
$$630$$ 0 0
$$631$$ 21.4448 + 37.1435i 0.853705 + 1.47866i 0.877841 + 0.478952i $$0.158983\pi$$
−0.0241360 + 0.999709i $$0.507683\pi$$
$$632$$ 5.05693 8.75885i 0.201154 0.348409i
$$633$$ 0 0
$$634$$ −34.5577 −1.37246
$$635$$ 15.6963 0.622887
$$636$$ 0 0
$$637$$ −11.6114 20.1116i −0.460061 0.796850i
$$638$$ −43.0076 −1.70269
$$639$$ 0 0
$$640$$ −5.13806 8.89938i −0.203100 0.351779i
$$641$$ −11.2034 + 19.4048i −0.442507 + 0.766444i −0.997875 0.0651607i $$-0.979244\pi$$
0.555368 + 0.831605i $$0.312577\pi$$
$$642$$ 0 0
$$643$$ −2.71105 + 4.69568i −0.106914 + 0.185180i −0.914518 0.404544i $$-0.867430\pi$$
0.807605 + 0.589724i $$0.200763\pi$$
$$644$$ −0.905427 + 1.56824i −0.0356788 + 0.0617975i
$$645$$ 0 0
$$646$$ −0.323544 + 0.319708i −0.0127297 + 0.0125787i
$$647$$ −25.1940 −0.990477 −0.495238 0.868757i $$-0.664919\pi$$
−0.495238 + 0.868757i $$0.664919\pi$$
$$648$$ 0 0
$$649$$ −7.50430 + 12.9978i −0.294570 + 0.510210i
$$650$$ −4.47564 7.75203i −0.175549 0.304060i
$$651$$ 0 0
$$652$$ −11.3431 19.6469i −0.444231 0.769431i
$$653$$ −8.11903 −0.317722 −0.158861 0.987301i $$-0.550782\pi$$
−0.158861 + 0.987301i $$0.550782\pi$$
$$654$$ 0 0
$$655$$ 5.86776 + 10.1633i 0.229272 + 0.397112i
$$656$$ −0.405129 0.701703i −0.0158176 0.0273969i
$$657$$ 0 0
$$658$$ −68.0357 −2.65231
$$659$$ −6.73290 11.6617i −0.262277 0.454277i 0.704570 0.709635i $$-0.251140\pi$$
−0.966847 + 0.255358i $$0.917807\pi$$
$$660$$ 0 0
$$661$$ −4.51947 7.82796i −0.175787 0.304472i 0.764646 0.644450i $$-0.222914\pi$$
−0.940433 + 0.339978i $$0.889580\pi$$
$$662$$ −8.52701 + 14.7692i −0.331412 + 0.574022i
$$663$$ 0 0
$$664$$ −22.3743 −0.868289
$$665$$ −14.3543 3.93811i −0.556634 0.152713i
$$666$$ 0 0
$$667$$ −1.18715 + 2.05620i −0.0459665 + 0.0796163i
$$668$$ −11.4653 + 19.8585i −0.443606 + 0.768348i
$$669$$ 0 0
$$670$$ 6.09394 10.5550i 0.235429 0.407776i
$$671$$ −9.39729 16.2766i −0.362779 0.628351i
$$672$$ 0 0
$$673$$ 13.6988 0.528048 0.264024 0.964516i $$-0.414950\pi$$
0.264024 + 0.964516i $$0.414950\pi$$
$$674$$ −21.3517 36.9823i −0.822438 1.42450i
$$675$$ 0 0
$$676$$ 14.5157 0.558298
$$677$$ 11.6030 0.445941 0.222970 0.974825i $$-0.428425\pi$$
0.222970 + 0.974825i $$0.428425\pi$$
$$678$$ 0 0
$$679$$ 15.2762 26.4591i 0.586246 1.01541i
$$680$$ 0.0403154 + 0.0698283i 0.00154602 + 0.00267779i
$$681$$ 0 0
$$682$$ 2.32039 4.01904i 0.0888524 0.153897i
$$683$$ 25.5290 0.976840 0.488420 0.872609i $$-0.337574\pi$$
0.488420 + 0.872609i $$0.337574\pi$$
$$684$$ 0 0
$$685$$ −10.2572 −0.391908
$$686$$ −7.17528 + 12.4279i −0.273953 + 0.474501i
$$687$$ 0 0
$$688$$ −14.8570 25.7330i −0.566416 0.981062i
$$689$$ −13.4518 + 23.2993i −0.512474 + 0.887631i
$$690$$ 0 0
$$691$$ −46.1415 −1.75530 −0.877652 0.479298i $$-0.840891\pi$$
−0.877652 + 0.479298i $$0.840891\pi$$
$$692$$ 10.5515 0.401106
$$693$$ 0 0
$$694$$ 25.1631 + 43.5838i 0.955178 + 1.65442i
$$695$$ 21.8088 0.827255
$$696$$ 0 0
$$697$$ 0.00475566 + 0.00823705i 0.000180134 + 0.000312000i
$$698$$ −0.00862000 + 0.0149303i −0.000326272 + 0.000565119i
$$699$$ 0 0
$$700$$ 2.09550 3.62951i 0.0792024 0.137183i
$$701$$ 0.219837 0.380768i 0.00830312 0.0143814i −0.861844 0.507173i $$-0.830690\pi$$
0.870147 + 0.492792i $$0.164024\pi$$
$$702$$ 0 0
$$703$$ −7.30277 27.9192i −0.275429 1.05299i
$$704$$ −4.73024 −0.178277
$$705$$ 0 0
$$706$$ 5.46650 9.46826i 0.205735 0.356343i
$$707$$ −3.73997 6.47782i −0.140656 0.243624i
$$708$$ 0 0
$$709$$ 19.4677 + 33.7191i 0.731125 + 1.26635i 0.956403 + 0.292051i $$0.0943377\pi$$
−0.225278 + 0.974295i $$0.572329\pi$$
$$710$$ −15.1084 −0.567007
$$711$$ 0 0
$$712$$ 7.75988 + 13.4405i 0.290814 + 0.503704i
$$713$$ −0.128100 0.221876i −0.00479739 0.00830932i
$$714$$ 0 0
$$715$$ 21.7081 0.811835
$$716$$ −3.78373 6.55361i −0.141404 0.244920i
$$717$$ 0 0
$$718$$ −16.0073 27.7255i −0.597388 1.03471i
$$719$$ −11.5179 + 19.9496i −0.429546 + 0.743995i −0.996833 0.0795252i $$-0.974660\pi$$
0.567287 + 0.823520i $$0.307993\pi$$
$$720$$ 0 0
$$721$$ −35.8219 −1.33408
$$722$$ 0.407100 34.1305i 0.0151507 1.27021i
$$723$$ 0 0
$$724$$ −12.3092 + 21.3202i −0.457469 + 0.792360i
$$725$$ 2.74750 4.75882i 0.102040 0.176738i
$$726$$ 0 0
$$727$$ 22.2700 38.5727i 0.825948 1.43058i −0.0752445 0.997165i $$-0.523974\pi$$
0.901193 0.433419i $$-0.142693\pi$$
$$728$$ −11.8092 20.4542i −0.437678 0.758081i
$$729$$ 0 0
$$730$$ −21.0117 −0.777677
$$731$$ 0.174401 + 0.302071i 0.00645044 + 0.0111725i
$$732$$ 0 0
$$733$$ 34.2392 1.26465 0.632326 0.774702i $$-0.282100\pi$$
0.632326 + 0.774702i $$0.282100\pi$$
$$734$$ −8.80612 −0.325040
$$735$$ 0 0
$$736$$ −1.32072 + 2.28756i −0.0486826 + 0.0843207i
$$737$$ 14.7786 + 25.5974i 0.544378 + 0.942891i
$$738$$ 0 0
$$739$$ 2.42166 4.19444i 0.0890823 0.154295i −0.818041 0.575160i $$-0.804940\pi$$
0.907123 + 0.420865i $$0.138273\pi$$
$$740$$ 8.12555 0.298701
$$741$$ 0 0
$$742$$ −33.1230 −1.21598
$$743$$ 6.53384 11.3169i 0.239703 0.415178i −0.720926 0.693012i $$-0.756283\pi$$
0.960629 + 0.277834i $$0.0896165\pi$$
$$744$$ 0 0
$$745$$ −10.3765 17.9727i −0.380167 0.658468i
$$746$$ 11.6766 20.2245i 0.427512 0.740473i
$$747$$ 0 0
$$748$$ 0.310591 0.0113563
$$749$$ 46.7519 1.70828
$$750$$ 0 0
$$751$$ −4.24060 7.34493i −0.154742 0.268020i 0.778223 0.627988i $$-0.216121\pi$$
−0.932965 + 0.359967i $$0.882788\pi$$
$$752$$ −54.8798 −2.00126
$$753$$ 0 0
$$754$$ 24.5937 + 42.5975i 0.895648 + 1.55131i
$$755$$ 7.47548 12.9479i 0.272061 0.471223i
$$756$$ 0 0
$$757$$ 17.6798 30.6223i 0.642583 1.11299i −0.342271 0.939601i $$-0.611196\pi$$
0.984854 0.173386i $$-0.0554707\pi$$
$$758$$ −15.0286 + 26.0303i −0.545864 + 0.945464i
$$759$$ 0 0
$$760$$ −5.83502 1.60085i −0.211659 0.0580688i
$$761$$ −19.8496 −0.719547 −0.359773 0.933040i $$-0.617146\pi$$
−0.359773 + 0.933040i $$0.617146\pi$$
$$762$$ 0 0
$$763$$ −24.1657 + 41.8562i −0.874856 + 1.51529i
$$764$$ 10.4752 + 18.1435i 0.378978 + 0.656409i
$$765$$ 0 0
$$766$$ −26.8503 46.5061i −0.970141 1.68033i
$$767$$ 17.1652 0.619798
$$768$$ 0 0
$$769$$ −2.82265 4.88897i −0.101787 0.176301i 0.810634 0.585553i $$-0.199123\pi$$
−0.912421 + 0.409253i $$0.865789\pi$$
$$770$$ 13.3632 + 23.1457i 0.481575 + 0.834113i
$$771$$ 0 0
$$772$$ 8.92444 0.321198
$$773$$ 24.6102 + 42.6260i 0.885166 + 1.53315i 0.845523 + 0.533938i $$0.179289\pi$$
0.0396424 + 0.999214i $$0.487378\pi$$
$$774$$ 0 0
$$775$$ 0.296472 + 0.513505i 0.0106496 + 0.0184456i
$$776$$ 6.20979 10.7557i 0.222918 0.386106i
$$777$$ 0 0
$$778$$ 57.0088 2.04387
$$779$$ −0.688308 0.188838i −0.0246612 0.00676583i
$$780$$ 0 0
$$781$$ 18.3199 31.7310i 0.655539 1.13543i
$$782$$ 0.0225441 0.0390475i 0.000806175 0.00139634i
$$783$$ 0